Superconducting radio frequency accelerator cryomodules based on single cell cavities have been designed, but these designs have not included fundamental power couplers with sufficiently strong coupling to match a cavity for a 1-ampere (A) beam. Furthermore, existing designs have single cell cavities spaced at intervals of over 1.6 free space wavelengths, so that the effective accelerating gradient in such a design would be to less than 1.5 MeV/m even if adequate couplers could be incorporated. Existing designs do not offer simultaneously strong fundamental power coupling, superconducting radio frequency accelerating cavities, and high linear density of accelerating cells along a beam axis.